On Donaldson's flow of surfaces in a hyperkahler four-manifold

Details On Donaldson's flow of surfaces in a hyperkahler four-manifold On Donaldson's flow of surfaces in a hyperkahler four-manifold

2006-06-16

arxiv.org/abs/math/0606394v1

Math. Z. 256 (2007), no. 4, 769--787

Mathematics

Differential Geometry

19 pages

Scientific paper

We prove some basic properties of Donaldson's flow of surfaces in a hyperkahler 4-manifold. When the initial submanifold is symplectic with respect to one K\"ahler form and Lagrangian with respect to another, we show that certain kinds of singularities cannot form, and we prove a convergence result under a condition related to one considered by M.-T. Wang for the mean curvature flow.

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